Review of Submarine Out-of-Plane Normal Force and Pitching Moment

摘要

The normal force and pitching moment experienced by a submarine in a turn, or at an angle of drift, are called out-of-plane because they are loads induced in the vertical plane by a maneuver in the horizontal plane. They arise from the interaction of flow circulation generated by the sail with cross flow on the hull aft of the sail, i.e., the Magnus Effect. Smaller than the corresponding in-plane loads, side force, and yawing moment, the out-of-plane loads are nevertheless significant for good maneuverability and safety. Left uncorrected, they would result in a bow-up attitude and decrease in depth, but are generally not a significant problem for closed-loop control. However, while this response may assist recovery from a plane jam-to-dive, it could hinder covert recovery from a jam-to-rise. It is necessary to model out-of-plane loads in a numerical simulation. Experiments with a number of submarine configurations validate the previously proposed linear circulation distribution model, or a simple modification of it, for estimating the out-of-plane normal force and pitching moment arising from both drift and yaw rate. The effect of the tail does not appear to be greatly significant. Pitching moment may be underpredicted for submarines with a relatively small sail. A numerical circulation distribution model will be implemented in the DSSP21 maneuvering simulation code for estimating out-of-plane loads. In the longer term, the effect of full-scale Reynolds numbers should be investigated so that proper scaling can be applied to results from experimental and numerical models. (13 figures, 12 refs.).